The function of diorism in ancient Greek analysis (Q619763)

In the classical Greek method of approach to a geometric problem, \textsl{analysis} examines the properties a solution must have, while \textsl{synthesis} constructs a solution. But there is also another, less celebrated, component of the method: \textsl{diorism,} which deals with matters such as determining what and how many kinds of solutions exist and restrictions that apply to the solution(s). This article provides an in-depth look at diorism, with case studies from Archimedes and, especially, Apollonius.